## 155 Reputation

7 years, 235 days

## Getting a smooth DEplot3d from a stiff s...

Maple 18

I've been trying to make a smooth plot of some ODEs. It should show C rapidly increasing at the innitiation, until they get into a quassi steady state,  and then all three variables increase much slower. This should look like a roughly straight line that elbows sharply into a smooth curve.

Any attempt to DEplot3d it i've made either just shows the time before the quassi steady state is reached, so shows the straight line; or smooths that time together with the next period, making the straight line look like a part of the smooth curve.

Model := [diff(B[1](t), t) = k[a1]*C(t)*(R-B[1](t)-B[2](t))-k[d1]*B[1](t), diff(B[2](t), t) = k[a2]*C(t)*(R-B[1](t)-B[2](t))-k[d2]*B[2](t), diff(C(t), t) = (-(k[a1]+k[a2])*C(t)*(R-B[1](t)-B[2](t))+k[d1]*B[1]+k[d2]*B[2](t)+k[m]*((I)(t)-C(t)))/h];
DissMod := subs((I)(t) = 0, Model);
AssMod := subs((I)(t) = C[T], Model);

Pars := [k[a1] = 6*10^(-4), k[d1] = 7*10^(-3), k[a2] = 5*10^(-4), k[d2] = 10^(-2), R = .5, k[m] = 10^(-4), C[T] = 100, h = 10^(-6)]

StateSol := DEplot3d(subs(Pars, AssMod), [B[1](t), B[2](t), C(t)], t = 0 .. 1000, number = 3, B[1] = 0 .. .5, B[2] = 0 .. .5, [[B[1](0) = 0, B[2](0) = 0, C(0) = 0]], scene = [B[1](t), B[2](t), C(t)], maxstep = .1, maxfun = 0, method = l)

## plotting the intersection of two deforme...

Maple 18

I have two deformed planes, that i would like to draw with 3dplot, as well as drawing a curve marking their intersection.

the curves are given by the expressions:

C = -(k[d2]*B[2]+I*k[m]+k[d1]*B[1])/((B[1]+B[2]-R)*k[a1]+(B[1]+B[2]-R)*k[a2]-k[m]),

C = k[d1]*B[1]/(k[a1]*(R-B[1]-B[2]))

evaluated at

Pars := [k[a1] = 6*10^(-4), k[d1] = 7*10^(-3), k[a2] = 5*10^(-4), k[d2] = 10^(-2), R = .5, k[m] = 10^(-4), C[T] = 100, h = 10^(-6)]

with the variables B[1],B[2] and C within the bounds [0..0.5],[0..0.5],[0..100].

My method was to try and use solve to find a formula for the intersection curve- but i couldn't get 3dplot to plot it!

## exporting to latex...

Maple 2015

I have exported a maple document to latex, but it only shows the output of the commands used. Rather than the commands, and the procedures.

How do I get both to export together? and show up together?

## Describing the length of an equation...

My PhD involves generating equations that are very long, in some cases, more than 10 pages long.

For the reader its much more useful to have some of these equations described than presented. One of the descriptions I'd like to use is number of characters and intuitively the command Length feels like it should tell you the number of characters in an expr

However what is written on the help page for this function I don't understand:
https://www.maplesoft.com/support/help/maple/view.aspx?path=length

 For other objects, the length of each operand of expr is computed recursively and added to the number of words used to represent expr. In this way, the measure of the size of expr is returned.

then the example that is given is

 >length(x+2y) length(x+2y)
 99 (5)

Could anyone explain to me what is meant when it is said length(x+2y)=9? if I try an apply things recursively the expression with the most chatracters i can generate is "x+y+y"which is only 5 characters.

Is there another command that would be better suited to my purposes?

## Asterisk tickmarks in DEplot...

Maple 2015

I am trying to use y* to label a point on the axis of a graph made with DEplot, and am currently unable to.

with(DEtools);
NLC := diff(y(t), t) = k*(Am-y(t));
Am := 20; k := .1;
ivs := [y(0) = 10, y(0) = 30, y(0) = 50];
DEplot(NLC, y(t), t = 0 .. 20, ivs, tickmarks = [default, [20 = y^*]], font = [default, default, 30]);

makes y* apear as the label, as does the code

tickmarks = [default, [20 = y^&ast;]]

wheras if i remove the  marks I get an error

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